Complete energy spectrum is obtained for the quantum mechanical problem of N one dimensional equal mass particles interacting via potential $$V(x_1,x_2,...,x_N) = g\sum^N_{ i < j}{ 1\over (x_i-x_j)^2} - { \alpha\over \sqrt{ \sum_{ i < j} (x_i-x_j)^2}}$$ Further, it is shown that scattering configuration, characterized by initial momenta $p_i (i=1,2,...,N)$ goes over into a final configuration characterized uniquely by the final momenta $p'_i$ with $p'_i=p_{ N+1-i}$.
Categories: hep-th cond-mat nlin.SI solv-int